In this study, the authors propose a novel framework for audio source separation based on a cascaded non-negative matrix factorisation (NMF) using homotopy optimisation with perturbation and ensemble (HOPE) and denoising autoencoder. NMF using traditional optimisation has a problem of finding a global solution, and hence could not achieve complete separation of the sources from the mixture. This problem has been addressed using homotopy optimisation in this study. Subsequently, using denoising autoencoder the residual sounds that are usually observed in the separated sources are removed. The enhanced audio signals are filtered using Wiener techniques to obtain the separated signals. The homotopy-based NMF is applied for separating singing voice and drums from song samples using a single-channel mixture. The separated signals are compared with other NMF algorithms by using Blind Source Separation (BSS) Eval objective quality measures. The NMF with HOPE and denoising autoencoder is shown to provide an improvement of up to 6 dB in comparison with other NMF algorithms.